12 22 29 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 22   c = 29

Area: T = 120.7832604294
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 22.24987765252° = 22°14'56″ = 0.38883144049 rad
Angle ∠ B = β = 43.96597525293° = 43°57'35″ = 0.767724242 rad
Angle ∠ C = γ = 113.7911470945° = 113°47'29″ = 1.98660358287 rad

Height: ha = 20.1330434049
Height: hb = 10.9880236754
Height: hc = 8.33298347789

Median: ma = 25.03299820216
Median: mb = 19.27443352674
Median: mc = 10.18657743937

Inradius: r = 3.83443683903
Circumradius: R = 15.84766528453

Vertex coordinates: A[29; 0] B[0; 0] C[8.63879310345; 8.33298347789]
Centroid: CG[12.54659770115; 2.7776611593]
Coordinates of the circumscribed circle: U[14.5; -6.39326838183]
Coordinates of the inscribed circle: I[9.5; 3.83443683903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.7511223475° = 157°45'4″ = 0.38883144049 rad
∠ B' = β' = 136.0440247471° = 136°2'25″ = 0.767724242 rad
∠ C' = γ' = 66.20985290545° = 66°12'31″ = 1.98660358287 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 12 ; ; b = 22 ; ; c = 29 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12+22+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-12)(31.5-22)(31.5-29) } ; ; T = sqrt{ 14588.44 } = 120.78 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120.78 }{ 12 } = 20.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120.78 }{ 22 } = 10.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120.78 }{ 29 } = 8.33 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 22**2+29**2-12**2 }{ 2 * 22 * 29 } ) = 22° 14'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12**2+29**2-22**2 }{ 2 * 12 * 29 } ) = 43° 57'35" ; ; gamma = 180° - alpha - beta = 180° - 22° 14'56" - 43° 57'35" = 113° 47'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120.78 }{ 31.5 } = 3.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12 }{ 2 * sin 22° 14'56" } = 15.85 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 29**2 - 12**2 } }{ 2 } = 25.03 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 12**2 - 22**2 } }{ 2 } = 19.274 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 12**2 - 29**2 } }{ 2 } = 10.186 ; ;
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